Remark 1 The midpoint rule and the trapezoidal rule are not the only numerical integration methods that can be applied to discretize the optimization problem in (REF ). However, any such integration method is required to be explicit in order to apply the Levenberg-Marquardt algorithm later in this section. Alternatively, we may change the problem formulation in (REF ) by replacing all integrals by finite, weighted sums of function evaluations, as in [1]}, for instance. However, the solution of this altered optimization problem may not correspond to the solution of (REF ), not even in the limit.

